Global maximal estimates for solutions to the Schrödinger equation

• Autorzy: Per Sjölin
• Języki publikacji: EN

Abstrakty

EN

Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.

Kategorie tematyczne

• 35Q40: PDEs in connection with quantum mechanics
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 110
• Numer: 2
• Strony: 105-114

Daty

wydano

1994

otrzymano

1993-02-02

Twórcy

autor

Per Sjölin

• Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Bibliografia

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• [2] A. Carbery, Radial Fourier multipliers and associated maximal functions, in: Recent Progress in Fourier Analysis, Proc. Seminar on Fourier Analysis held in El Escorial, Spain, 1983, North-Holland Math. Stud. 111, North-Holland, 1985, 49-56.
• [3] L. Carleson, Some analytical problems related to statistical mechanics, in: Euclidean Harmonic Analysis, Proc. Seminars held at the Univ. of Maryland, 1979, Lecture Notes in Math. 779, Springer, 1979, 5-45.
• [4] M. Cowling, Pointwise behaviour of solutions to Schrödinger equations, in: Harmonic Analysis, Proc. Conf. Cortona, Italy, 1982, Lecture Notes in Math. 992, Springer, 1983, 83-90.
• [5] B. E. J. Dahlberg and C. E. Kenig, A note on the almost everywhere behaviour of solutions to the Schrödinger equation, in: Harmonic Analysis, Proc. Conf. Univ. of Minnesota, Minneapolis, 1981, Lecture Notes in Math. 908, Springer, 1982, 205-209.
• [6] C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69.
• [7] C. E. Kenig, G. Ponce and L. Vega, Well-posedness of the initial value problem for the Korteweg-de Vries equation, J. Amer. Math. Soc. 4 (1991), 323-347.
• [8] C. E. Kenig and A. Ruiz, A strong type (2,2) estimate for a maximal operator associated to the Schrödinger equation, Trans. Amer. Math. Soc. 280 (1983), 239-245.
• [9] E. Prestini, Radial functions and regularity of solutions to the Schrödinger equation, Monatsh. Math. 109 (1990), 135-143.
• [10] P. Sjölin, Convolution with oscillating kernels, Indiana Univ. Math. J. 30 (1981), 47-55.
• [11] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715.
• [12] P. Sjölin, Radial functions and maximal estimates for solutions to the Schrödinger equation, J. Austral. Math. Soc., to appear.
• [13] E. M. Stein, Oscillatory integrals in Fourier analysis, in: Beijing Lectures in Harmonic Analysis, Ann. of Math. Stud. 112, Princeton Univ. Press, 1986, 307-355.
• [14] L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874-878.